A thorough numerical investigation was performed for the two-dimensional convective heat transfer of a circular cylinder in a Couette flow close to a wall in order to study the hot-wire near-wall correction. A finite-volume Navier-Stokes solver enhanced by local block refinement and multigrid acceleration guaranteed highly accurate and efficient computational results. Unlike all previous numerical simulations, a more realistic model was used in the present study by taking the heat transfer in the solid wall into account to bridge the discrepancy between the previous theoretical models and the real situation. The computed results from the present investigation show good agreement with experimental data in the literature. Reference correction curves for hot-wire anemometers with respect to different wall materials (e.g., aluminum, glass, Perspex, air, etc.) were obtained.